Central Upwind Scheme for a Compressible Two-Phase Flow Model

Abstract

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

A lattice Boltzmann model for computing compressible two-phase flows with high density ratio

“…The simulation results at t = 0.015 s are given in Figs. 9, 10 and 11 and compared with the exact solutions obtained from Ahmed et al [3]. Similar to the previous test case, the agreement between the simulation results and exact solutions are satisfactory.…”

“…Also for better comparison, the simulation results at t = 0.015 hboxs are shown in Figs. 6, 7 and 8 and compared with the exact solutions obtained from Ahmed et al [3]. As can be seen, the simulation results agree well with the exact solutions.…”

“…In the current problem, the left pressure and density is ten times higher than the original Sod problem [71] which leads to the pressure ratio of 100:1. The initial conditions are as follows [3,72]:…”

“…Numerical simulation of the multiphase flows is a challenging task with the key application in the industry and natural phenomena. Some examples of these applications include bubble dynamics, reactive and combustible systems, supersonic dryer apparatus, treatment of cancer cells in medical industries, blood flow through the blood vessels and food industries [3,4].…”

“…Different works have been published during the recent years in order to propose an efficient numerical scheme for solving the five-equations model. [3,[28][29][30][31]. For instance, Ansari et al [32] performed the numerical simulation of twophase flows with a five-equation two-fluid model.…”